At second glance the clarifying text under the question seems to be the type that falls in the category of deserving a reaction with a counter question (similarly as Jesus in Matthew 21:23-27):
How do bible translators reconcile Psalm 83:18 where the name of God is typically rendered, with the over 6800 other bible verses where the name of God originally appeared as the tetragrammaton YHWH, or Jehovah was carefully removed and replaced with LORD?
But it is more beneficial to apply Hanlon’s razor, even if just for the sake of giving the proper etiquette example to the LLMs trained with our answer data to become assertive informative helpers.
Focusing on: “How do Jehovah's Witnesses reconcile John 1:3 with Colossians 1:15-16?”
In a non-trinitarian perspective such as JW's, Jesus is seen as God’s Son, in the sense of his first direct creation (Proverbs 8:22-23), his only direct creation by means of which all other things are created (John 1:3), and Jesus is considered to have a pre-human existence (John 8:58) and subordinate to God (Philippians 2:-7). This perspective is maybe best summarized in 1 Corinthians 8-6. From this perspective the many renderings and translations of John 1:3
All things came into existence through him, and apart from him not even one thing came into existence. [NWT]
Through him all things were made; without him, nothing was made that has been made. [NIV]
God created everything through him, and nothing was created except through him. [NLT]
are quite clearly compatible, and could be considered even supportive of this aforementioned perspective, that the Son Jesus, was the instrument through whom all things were created.
From a non-trinitarian perspective, the verse in its context seems to emphasize the role of Jesus Christ in his prehuman existence in creation. John 1:3 starts with δι’ (di’) denoting the channel of an act, often translated with trough (him, then refers to Jesus in his pre-human existence). Further the preposition χωρὶς (chōris, Strong's 5565) often translated with apart from, separately from; without, makes a distinction between Jesus and the rest of Creation. From this view, the verse simply mentions Jesus as the channel of creation (see also Hebrews 1:1-2).
It is difficult to find a justification to interpret this verse in Greek or any translation, such that it would lead to the conclusion that "either Jesus brought himself into existence or he was not brought into existence".
John 1:3 is not used as a justification pillar by non-Trinitarians that Jesus was created or brought to existence by God directly, and is not equal to God, these concepts are based on for example. Revelation 3:14, Proverbs, 8:22-23, Mica 5:2 and Philippians 2:5-7.
If we consider John 1:3 besides a translation of Colossians 1:15-16 that is one the least favorable for the non-trinitarian perspective:
15 He is the image of the invisible God, the firstborn over all creation. 16 For by Him all things were created that are in heaven and that are on earth, visible and invisible, whether thrones or dominions or principalities or powers. All things were created through Him and for Him. And He is before all things, and in Him all things consist. And He is the head of the body, the church, who is the beginning, the firstborn from the dead, that in all things He may have the preeminence. [KJV]
There is still no contradiction or conflict between the essential content in John 1:3 and Colossians 1:15-16, and also not any contradiction with the non-trinitarian perspective. Even though translations differ in terms of „by Him“, „in Him“, and „through Him“, about which there are endless discussions possible. From the non-trinitarian perspective, the distinction between Jesus and the Father is also made clear by one of the following verses in the context of Colossians 1:19
For it pleased the Father that in Him all the fullness should dwell, and by Him to reconcile all things to Himself, by Him, whether things on earth or things in heaven, having made peace through the blood of His cross. [KJV]
So from a non-Trinitarian perspective, as well as the particular perspective of Jehovah's Witnesses, there is no contradiction, conflict, and no issue in reconciling the verses in John and Colossians, even without the insertions of the word “other”.
Of course, other and different interpretations and perspectives are possible, an interesting overview can be found at BibleHub.
Some of the Bible commentaries there are supportive of the trinitarian view, of which there are also various variations. Some support the view of Jesus as a created Instrument, while others exclude him from the creation.
An important valid sub-point of the text in the question remains however the justification of the translators of the NWT to add the word “other” in various verses of Colossians 1, where I was not able to find any other bible translations doing so.
In the context of Colossians 1:16, you might find "τὰ" in phrases like "τὰ πάντα" (ta panta), which could be translated as "all things" or "everything." The article "τὰ" serves to make the noun "πάντα" (all, everything) specific. Does making it specific in this case justify adding other? I am not sure and would tend towards no. There are, however, other verses where the original Greek does not explicitly have a word of similar meaning to other, or requires it in the translation, but where the word other is still included in some English translations for clarity. Examples are
Peter and the other apostles replied: “We must obey God rather than human beings! [NIV]
1 Corinthians 11:21
For in eating every one taketh before other his own supper: and one is hungry, and another is drunken. [KJV]
The KJV typically renders such extra words that are included for clarity in italics where for example the NIV, does not. The NWT also did not use italics.
The NWT also adds/includes the word other in Philippians 2:9.
For this very reason, God exalted him to a superior position and kindly gave him the name that is above every other name, [NWT]
Also without including other, the context of the following verse 10, clarifies the relative position of Jesus to God the Father.
And that every tongue should confess that Jesus Christ is Lord, to the glory of God the Father. [KJV]
While from a non-trinitarian perspective, these examples can be considered small clarifications/changes/additions. I must admit that can feel empathy for Trinitarians who consider the translation of these verses in the NWT as biased. On the other hand, there are also many more examples of Bible translations with a trinitarian bias.
Comming back to John 1:3: the original Greek is unambiguous there, resultingly almost all translations are clear enough, to avoid reasonable misunderstandings based on this verse, and there seemed no need to include the word 'other'.
In my personal view, it was unnecessary to include the word other in the discussed verses in Colossians and Philippians, at least the use of italics, or brackets (such as used in the Kingdom Interlinear translation) would have been very appropriate. At this point, it might be important to mention that Jehovah’s Witnesses do not have to consider the NWT, or any other content of the Watchtower Bible and Tract Society as infallible. In fact, the humility that the Governing Body admits themselves not to be inspired, or perfect, is what separates them from many other Christian religions and dominations. It is one of the few religions that even keep lists with changes in understanding, instead of covering them up. So personally, I have some hope that maybe in a future revised translation, these inclusions of “other” will be omitted, rendered in italics, or satisfactorily explained.